What is the value of (2 + 3i)(2 - 3i)? (2019)

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Question: What is the value of (2 + 3i)(2 - 3i)? (2019)

Options:

Correct Answer: 13

Exam Year: 2019

Solution:

Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.

What is the value of (2 + 3i)(2 - 3i)? (2019)

What is the value of (2 + 3i)(2 - 3i)? (2019)

Step 1: Identify the expression we need to calculate: (2 + 3i)(2 - 3i).
Step 2: Recognize that this expression is in the form of (a + b)(a - b), where a = 2 and b = 3i.
Step 3: Use the difference of squares formula: (a + b)(a - b) = a² - b².
Step 4: Calculate a²: 2² = 4.
Step 5: Calculate b²: (3i)² = 9i². Since i² = -1, this becomes 9(-1) = -9.
Step 6: Substitute the values into the formula: 4 - (-9).
Step 7: Simplify the expression: 4 + 9 = 13.

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